Chapter 3: The World of Numbers — Online MCQ Test
MATHS · Grade 9 · CBSE(NCERT)
Practice Chapter 3: The World of Numbers with a free chapter-wise online MCQ test.
This chapter covers: Real Numbers Rational Numbers Irrational Numbers Number Line Decimal Expansion Square Root Spiral Proof Surds Exponents Root Two Understanding rational and irrational numbers logic....
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 3: The World of Numbers — Important Questions & Answers
Which of the following is a rational number?
- A. √2
- B. π
- C. 3/7
- D. √5
Answer: C. 3/7
A rational number can be expressed as p/q where p and q are integers and q ≠ 0. 3/7 fits this definition, while √2, π, and √5 are irrational numbers.
A rational number can be expressed as p/q where p and q are integers and q ≠ 0. 3/7 fits this definition, while √2, π, and √5 are irrational numbers.
The decimal expansion of an irrational number is:
- A. Terminating
- B. Non-terminating and repeating
- C. Non-terminating and non-repeating
- D. Both terminating and repeating
Answer: C. Non-terminating and non-repeating
Irrational numbers have decimal expansions that never end and never repeat in a pattern, distinguishing them from rational numbers which either terminate or have repeating decimals.
Irrational numbers have decimal expansions that never end and never repeat in a pattern, distinguishing them from rational numbers which either terminate or have repeating decimals.
Which statement is correct about the number √2?
- A. It is a rational number that can be written as 1.414
- B. It is an irrational number with non-terminating, non-repeating decimal expansion
- C. It is a rational number equal to 1.414214...
- D. It is a natural number between 1 and 2
Answer: B. It is an irrational number with non-terminating, non-repeating decimal expansion
√2 is irrational because it cannot be expressed as a ratio of two integers, and its decimal expansion (1.41421356...) neither terminates nor repeats.
√2 is irrational because it cannot be expressed as a ratio of two integers, and its decimal expansion (1.41421356...) neither terminates nor repeats.
If a = 2^(1/3) and b = 2^(1/2), then which of the following is true?
- A. a > b
- B. a < b
- C. a = b
- D. Cannot be determined
Answer: B. a < b
2^(1/3) ≈ 1.26 and 2^(1/2) ≈ 1.41. Since 1/3 < 1/2 and the base is 2 > 1, we have 2^(1/3) < 2^(1/2), so a < b.
2^(1/3) ≈ 1.26 and 2^(1/2) ≈ 1.41. Since 1/3 < 1/2 and the base is 2 > 1, we have 2^(1/3) < 2^(1/2), so a < b.
Consider the following statements: I. Every integer is a rational number II. Every rational number is a real number III. Every real number is a rational number Which statements are true?
- A. Only I and II
- B. Only II and III
- C. Only I and III
- D. All three are true
Answer: A. Only I and II
Statement I is true: integers can be expressed as p/1. Statement II is true: both rational and irrational numbers are real. Statement III is false: irrational numbers are real but not rational.
Statement I is true: integers can be expressed as p/1. Statement II is true: both rational and irrational numbers are real. Statement III is false: irrational numbers are real but not rational.